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Corporate dividend policy and the partial adjustment model
J ECO BUSN 1991; 43:165-178
165
Corporate Dividend Policy and the Partial Adjustment Model Michael T. Bond and Mbodja Mougou~
This article critiques Lintner's partial adjustment dividend model in terms of characterizing corporate dividend policy. It is first shown that many combinations of target rates and speeds of adjustment will produce the same stream of cash dividends over time. It is then established empirically from earnings and dividend data that the partial adjustment model gives results that are not unique.
I. Introduction Dividend policy has long been a subject of interest to firms, their stockholders, analysts, and academic researchers.t Aspects of dividend policy that have been examined include the implications of differential taxation of dividends and capital gains (Miller and Modigliani 1961), uncertainty about retention as opposed to cash payments to shareholders (Gordon 1962), preferred habitats of stockholders (Miller and Modigliani 1961), and optimal payment ratios (Walter 1963), and the adjustment process in reaching an optimal payout ratio (Lintner 1956). The last topic, the adjustment process in moving to a desired dividend payont ratio, is the subject of this research. In particular, this study will examine whether the speed of adjustment and target dividend payout rates implied in the partial adjustment model are in fact an accurate characterization of corporate dividend policy.
II. Literature Review There is considerable literature on the adjustment process of firms to a target level of dividends. For example, Lintner (1956) argued that investors will welcome the decision of a firm to change its dividends only if the dividends are related to the firm's earnings or some other public information pertaining to the company. He reasoned that a corporation would have a target dividend payout ratio based on the company's policy regarding internal financing and the cash requirements of its owners. Because many firms are concerned that dividends be stable and because forecasting earnings is
Address reprint requests to Michael T. Bond, PhD, or Mbodja Mougou~, PhD, Department of Finance, Cleveland State University, Cleveland, Ohio 44115. i See, for example, James S. Ang (1987) for an excellent review of the literature on the dividend debate.
Journal of Economicsand Business © 1991 Temple UniversiW
0148-6195/91/$03.50
M.T. Bond and M. Mougou6
166
difficult, Lintner argued that a corporation would adjust the amount paid shareholders over a period of time rather than abruptly. He thus characterized dividend policy by a target payout ratio, that is, a percentage of earnings per share (EPS) and the percentage adjustment to that target rate in each time period. Using aggregated data on corporate earnings and dividends, Lintner tested his proposition empirically and found that the partial adjustment model predicted dividend payments more accurately than "naive" models. Additional research on the partial adjustment model was carried out by Fama and Babiak (1968) (henceforth FB). Using data on individual firms over a 20 year period, FB tested Lintner's propositions and reported a mean speed of adjustment of 0.32 and a sample target ratio of 0.52. FB also examined several alternative dividend models and concluded that Lintner's model predicts dividends better than other models tested. Later research on the partial adjustment model by Fama (1974) indicated roughly the same findings as the FB study. In line with the assertions of Lintner (1956), the results of the work of Sibley and Hobson (1979) indicated that the partial adjustment model explained a higher portion of bank dividend changes than did several other forecasting models. Partington (1984) confirmed that firms apparently targeted dividend payout ratios. Using a survey of 93 large companies, he determined that around 60% of the firms had an explicit target payout ratio, the objective being to distribute about half of the firm's profits as dividends. Partington also reported that approximately, one third of all firms he studied had altered their targets significantly over the 1965-1980 time period. Baker, Edelman, and Farrelly (1985) sampled corporate financial managers on dividend policy. Analysis of the survey indicated that the primary determinants of dividend policy were quite similar to those suggested by Lintner (1956), specifically that firms target a payout ratio and adjust to it slowly over time. Farrelly and Baker (1989) also conducted a survey of institutional investors. Their findings indicated that these sophisticated investors believe that dividend policy affects stock prices and that, in line with the Lintner hypothesis, dividend consistency is of utmost importance. Recently, Bowers, Moran, and Forbes (1987) (henceforth BMF) have challenged the assertions of Lintner (1956) and Fama (1974) with regard to the partial adjustment model. They argue that the partial adjustment model is useful only if the differences in estimated parameters reflect meaningful differences in corporate dividend policy. They then show that dividend payments produced by any target rate and speed of adjustment can be duplicated by using an infinite number of alternative parameter pairs. On the basis of these results, BMF conclude that the partial adjustment model is not useful in explaining corporate dividend policy. The present study will apply the methodology proposed by BMF to earnings and dividend data from a sample of U.S. manufacturing firms to ascertain if the partial adjustment model is an accurate characterization of their dividend policy formulation.
III. The Partial Adjustment Model The partial adjustment model suggested by Lintner (1956) assumes the target level of dividends is given by (1): D*=rE
t
0 < r _ < 1,
(1)
where D* represents the optimal value of dividends associated with the current level of
Dividend Policy and the Partial Admustment Policy
167
earnings Et, and r is the target and, presumably, optimal payout ratio. The change in dividends as a firm moves to the target payout rate is given in (2): Dt - Dr-, = C(D*t - Dt-1) + (t
0 < c <- 1;
(2)
where c is the speed of adjustment and {~t} is an iid innovation sequence. Substituting and moving the lagged term to the right side of the equality in (2) results in (3): (3)
D t = ( c r ) E t + (1 - c ) D , _ , + ~t.
Previous work on the partial adjustment model essentially involved estimating the parameters of (3) and then a discussion on implied dividend policy in the context of the estimated values of c and r. This analysis is meaningful if a given stream of earnings and dividends implies unique values of c and r. If, however, consecutive earnings are related in a linear manner, as shown in (4), an infinite number of c and r pairs will produce the same dividend stream: E t = (1 + g ) E , _ 1,
(4)
where g is a constant growth rate. Recursive substitution for lagged dividends in (3) gives an infinite distributed lagged model, seen in (5): D, = ( c r ) E , + (1 - c ) ( c f ) E t _ 1 41- (1 - c)2(cr)Et_2 + . . . +~t.
(5)
If (4) holds through time, (5) may be expressed as (6): Oo
D, = ( c r ) E o ~
(1 + g ) t - i ( 1
- c ) i ~ t- ~,.
(6)
i=0
By recognizing the equality in (7),
i=0
(1 + g ) ' - l ( l
•
- c)'=
[(1 + g)'l
[(c+g)/(1
+g)]'
(7)
(6) can be expressed as (8):
[(1 + g)'] Dr= (cr)E°[(c+g)/(1
+g)]
+~t"
(8)
Given the equality in (4), dividends in period t can be expressed as (9): O t =
e t ( c r ) / [ ( c + g ) / ( 1 + g)] + ~t.
(9)
Given a constant growth in earnings it is obvious that there is a one-for-one relationship between dividends and the partial adjustment policy. Division of both sides
M. T. Bond and M. Mougou6
165
Table 1. Earnings and Dividends for the Constant Growth Partial Adjustment Model (E~ = $1,000, g = 5%, c = 25%, r = 40%) Period
Earnings
Dividends
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
$1,000.00 1,050.00 1,102.50 1,157.63 1,215.51 1,276.28 1,340.10 1,407.10 1,477.46 1,551.33 1,628.89 1,710.34 1,795.86 1,885.65 1,979.93 2,078.93 2,182.87 2,292.02 2,406.62 2,526.95
$350.00 367.50 385.88 405.17 425.43 446.70 469.03 492.49 517. l 1 542.97 570.11 598.62 628.55 659.98 692.98 727.63 764.00 802.21 842.32 884.43
N o t e . E t is earnings at time t ffi 1, g is a constant growth rate, c is the speed of adjustment in the partial adjustment model, and r is the assumed target payout rate.
by current earnings gives (10):
D,I , =
+ g)/(1 + g)] +
(10)
where et is a function of ~t and is also iid. Given that g is a constant and that the c and r terms are established by the firm's management, dividends will be a constant portion of earnings over time. If the dividend payout ratio D / E is defined as k, (10) becomes (11):
k = ( c r ) / [ ( c + g ) / ( 1 + g)] + ~t, E(k) = (cr)/[(c + g)/(1 + g)],
and
(11) (12)
where E(k) is the expected value of k, the payout ratio. Given the equality in (4), no single c and r pair will uniquely describe the firm's series of dividends or its payout ratio over time. For example, assume earnings at t = 1 are $1,000 and g = 5 percent. Assume a target payout rate of 40 percent and a speed of adjustment of 25 percent. Dividends, as implied by (9), are 35 percent of earnings in each period. Dividends based on these values are generated for a 20-year period and are reported in Table 1. A set of alternative target rate and speed of adjustment pairs that produce the same dividends as r = 40 percent and c = 25 percent can be found by setting k = 35 percent, g = 5 percent, allowing c to vary from - 1 to 1, and solving (9) for r. Figure 1 and Table 2 present these solution pairs. It is easily shown that they produce the same dividends as the initial c-r pair if applied to any earnings stream. Note that the asymptotic relationship between c and r values in Figure 1 is consistent with the above data. The latter observation lends additional support to the assertion of BMF that there are many c and r pairs, that are consistent with the partial adjustment model. It should
169
Dividend Policy and the Partial Admustmem Policy Ill
1.00
0.75 C 0.50
0.25
0-00
o.25
o:'3o
o:35
o:,o
o. ,5
o:5o
o.55
R Figure 1. Graph of
c-r
pairs for hypothetical 5 percent g, .35 payout.
be recognized that the above analysis does not imply that the partial adjustment model is not useful in forecasting dividend payments. Rather, it suggests that firms that exhibit autoregression in earnings over time can produce the same dividend payout ratio with an infinite combination of c - r values. The implication for firms in the autoregressive category, then, is that a particular c - r value is not the only policy combination that will produce the firm's desired payout ratio. It then follows that statistical estimates of the c - r values in Lintner's model may not be unique measures of corporate dividend policy. The present study examines the applicability of the BMF hypothesis to corporate dividend policy.
IV. The Empirical Results The Data Annual data from the Compustat tapes were collected for a sample of U.S. manufacturing firms. Annual data are used instead of quarterly data because of the relative inertia in quarterly dividend payments and because the time-series literature on interim corporate earnings has concluded that quarterly earnings contain significant amounts of
M. T. Bond and M. M o u g o u 6
170
T a b l e 2. Equivalent Partial Adjustment Policies ( k = 3 5 % , g = 5%) c -
1.00 -0.90 -0.80 - 0.70 0.60 - 0.50 0.40 - 0.30 - 0.20 -0.10 0.00 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 -
-
r .3166 .3148 .3125 .3095 .3055 .3000 .2916 .2777 .2500 .1666 Undefined .5000 .4166 .4000 .3888 .3750 .3666 .3611 .3571 .3541 .3518 .3500
Note. k is the actual payout ratio, g is a constant growth rate, c is the speed of adjustment in the partial adjustment model, and r is the implied target payout rate .......
noise or possess seasonal characteristics. 2 These factors could obscure existing relationships and lead to spurious results. The use of annual data is likely to minimize these problems. The sample was limited to firms reporting positive earnings (net income before extraordinary items) and having paid dividends every year over the 1968-1987 20-year time period covered in the present study. These criteria results in 430 firms.
Testing the Hypothesis
BMF essentially assert that if any c and r pair fits a firm's dividends and earnings pattern and earnings are determined autoregressively over time, then there will be many c and r pairs that fit the data. Using the Box and Jenkins (1976) procedure and the Augmented Dickey-Fuller test for unit roots as described in Engle and Granger (1987) resulted in the finding that only 310 of the 430 firms selected had earnings series behavior that follows AR(1) stationary processes. Our final sample thus includes only these 310 firms whose earnings exhibited significant first-order autocorrelation. For each of the 310 firms in the final sample the correlation coefficient between E t and Dr-i was also calculated. Figure 2 shows the frequency distribution of the simple correlation coefficient between E t and D t_ 1 for these sample firms. Clearly, high levels of correlation are present between E t and D t_ l, the explanatory variables of the
2 See, for example, Brown and Rozeff (1979), Foster (1977), Griffin (1977), and Lorek (1979).
Dividend Policy and the Partial Admustment Policy
171
0
0
~D
~5
0
r
0~ ~3
W
z LLJ
"'8 w~ C13
c~
Z
= o ""
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56 ~
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172
M.T.
Bond and M. Mougou~
0.7 ÷ 4" 4-
0.5. 0.4. C 0.3,
++ 4-
O.a.
0.1
4.
4'
4-
4" 4-
.I"
÷
4,
4"
0.0 0.00
4"
o; o
o;a5
o;75
4"
i:oo
i:a
l.oo
R Figure 3. Relationship between
c-r
pairs for . 3 5 - . 4 0 payout ratios.
partial adjustment model. 3 As is always the case, the question whether the resulting multicoUinearity problem is sufficient to impair the usefulness of the model is an empirical one. For example, multicollinearity frequently results in high standard errors of the estimates and correspondingly low t statistics; however, as noted by Maddala (1977), it is possible to have statistically significant t statistics even in the presence of high degrees of multicollinearity. The results of this correlation can be seen when the 310 firms in the final sample are divided into 2~) mutually exclusive groups by the most recent payout ratio, k. Firms with 0 < k < .05 are placed in Group 1, those with .05 < k < . 10 are assigned to the next group and so on. Figures 3-11 are plots of the c - r pairs from the payout groups with the most observations (k between .35 and .40, .40 and .45, .45 and .50, .50 and .55, .55 and .60, .60 and .65, .65 and .70, .70 and .75, .75 and .80). The plots have
3 Casual observation of the high versus low correlation firms indicated no easily identifiable variables (i.e., earnings growth, industry classification, etc.) that explain the difference in correlation values between E t and Dr_ j.
Dividend Policy and the Partial Admusunent Policy
173
I.,?,5
1.00.
0.75,
0.50
0.25. 4.
4.
4. 4"
4. 4.
'1'
4.
4.
0.00
~
o.o
~'.o
O'.5
~5
t
~'.o
2.,,
R
Figure 4. Relationship between
c-r
pairs for .4-.45 payout ratios.
4.
0"51 0.4 C
0.3,
4. ~W 4"
0.2.
4. ÷
0.I.
4-
4.
4.
0.0.
o.o
4.
o~5
1~o
~5
t
z~o
2.~
R
Figure $. Relationship between
c-r l~drs
for .45-.5 payout ratios.
174
M.T. Bond and M. Mougou6
1.0¢
0.75
C
0.,50. 4" 4" 4. 4¢¢ 4,
0.f¢5
4" 4"
÷ 41.
0.00
o.~s
o~oo
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l~oo
~'2o
~.~o
R
Figure 6. Relationship between
0.,~
c-r
pairs for .5-.55 payout ratios.
J
0A-.
÷
0.3.
4"
C
0.;~.
÷ ÷
0.1.
÷ 4" ÷
4.
0.0
o.o
ols
i~o
11~
z.o
R
Figure 7. Relationship between
c-r
pairs for .55-.6 payout ratios.
Dividend Policy and the Partial Admustment Policy
175
1.00
0.75.
C
0.50. 'W, 'i'4F
0.~5. ÷ ÷ 4, 4,4.
0.00 0.0
÷~
,I. t
z;o
5;0
~.5
R
Figure 8. Relationship between
c-r
pairs for .6-.65 payout ratios.
1.25.
!.00.
0.75 C 0.50
0.2.5 ÷
,I. "1-
÷ 4.
0.00.
, ,.,,
o.o
o.~
l:o
~.~
R Figure 9. Relationship between
c-r
pairs for .65-.7 payout ratios.
176
M.T. Bond and M. Mougoud
0.7 0.0 O.S 0.4 0.3 ¸
4.
0.'
4.
4"
4,
0.,1
4'
0.0 0.0
o17
o:e
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1~1
~.3
R
Figure 10. Relationship between
c-r
pairs for .7-.75 payout ratios.
1.0'
C
0.5
4~
44"4~
0.0. 0.0
ei~
~:o
t
t
7~5
lO.O
R
Figure 11. Relationship between
c-r
pairs for .75-.8 payout ratios.
Dividend Policy and the Partial Admustment Policy
177
two distinct features. First, many disparate c-r pairs are associated with roughly the same ex post payout ratio. Second, the c-r pairs in each figure roughly conform to the hyperbolic function of Figure 1. The constant-growth model proposed by BMF suggests that even though the partial adjustment model produces disparate parameter estimates, there may be no statistically significant difference in the dividend policies of these firms. The groups shown in Figures 3-11 are used to carry out further tests because they have the largest number of firms with similar ex post dividend payout ratio. The hypothesis that each firm's payout ratio is significantly different from the mean for each of these groups was examined. In each case the hypothesis that the difference is zero could not be rejected at the 5 percent level of significance. Because it may be possible that the empirical results reported here are sensitive to industry variations, the data were broken down by two-digit SIC industry codes with the requirement that each industry be composed of at least 20 firms. In this fashion, seven two-digit industries comprising approximately 46 percent of the sample were identified. The results were then summarized and analyzed on the basis of each industry. The empirical results were substantially the same as for all industries together. These findings lead to the tentative conclusion that the empirical results reported in the present study are robust to industry variations. In addition, the above results have important implications for investors. Those seeking a particular stream of cash dividends over time appear to have far more firm "choices" in companies able to produce their desired cash stream. Tables 1 and 2 clearly show that any of the values of target payout rate and speed of adjustment from a firm with a 5 percent earnings growth could provide the investor with the 35 percent payout ratio that is shown.
V. Conclusion This article demonstrates that two potential problems exist when the partial adjustment model is used to characterize the dividend policy of the individual firm. The first of these is that high degrees of correlation between the independent variables of the partial adjustment model may render the empirical results of such a model useless. This study also shows that autocorrelated earnings of firms result in an infinite number of pairs of speeds of adjustment and target payout rates that give identical dividend payout streams. Empirical tests with representative firms indicated that in many cases the partial adjustment model gives results that are not unique. It is probable, then, for the firms under consideration in this study, that the partial adjustment model does not generate unique measures of the dividend policy of the individual firm.
References Ang. J. S. 1987. Do Dividends Matter? A Review of Corporate Dividend Theories and Evidence. Monograph Series in Finance and Economics. New York: Center for the Study of Financial Institutions, New York University. Baker, K., Edelman, R., and Farrelly, G. Autumn 1985. A survey of management views on dividend policy. Financial Management 14: 78-84. Bowers, D., Moran, M., and Forbes, S. April 1987. The Appropriateness of the Partial-AdJttstmerit Dividend Model for Individual Firms. Unlmblhdtedmanuscript. Box, G. E. P., and JenkiM G. M. 1976. Time Series Analysis: Forecasting and Control(rev. ed.). San Francisco: Holden-Day.
178
M.T. Bond and M. Mougou6 Brown, L. D., and Roseff, M. S. Spring 1979. Univariate time-series models of quarterly accounting earnings per share: A proposed model. Journal of Accounting Research 17: 179-189. Engle, R. F., and Granger, C. W. J. 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica 55:251-276. Fama, E. June 1974. The empirical relationship between the dividend and investment decisions of firms. American Economic Review 64: 304-318. Fama, E., and Babiak, H. December 1968. Dividend policy: An empirical analysis. Journal of the American Statistical Association: 1132-1161. Farrelly, G., and Baker, K. Summer 1989. Corporate dividends: View of institutional investors. Akron Business and Economic Review 20: 89-100. Foster, G. January 1977. Quarterly accounting data: Time-series properties and predictive ability results. Accounting Review 52: 1-21. Gordon, M. 1962. The Investment, Financing, and Valuation of the Corporation. Homewood, Ill.): R. D. Irwin. Griffin, P. Spring 1977. The time-series behavior of quarterly earnings: Preliminary evidence. Journal o f Accounting Research 15: 71-83. Lintner, J. May 1956. Distribution of incomes of corporations among dividends, retained earnings, and taxes. American Economic Review 46: 97-113. Lorek, K. S. Spring 1979. Predicting annual net earnings with quarterly earnings time-series models. Journal of Accounting Research 16: 190-204. Maddala, G. S. 1977. Econometrics, New York: McGraw-Hill. Miller, M., and Modigliani, F. October 1961. Dividend policy, growth, and the valuation of shares. Journal of Business 34: 411-433. Partington, G. November 1984. Dividend policy and target payout rates. Accounting and Finance 24: 63-74. Sibley, A., and Hobson, H. Spring 1979. A test of selected models of bank dividend policy. Akron Business and Economic Review 10: 29-34. Walter, J. May 1963. Dividend policy: It's influence on the value of the enterprise. Journal of Finance: 280-291.
165
Corporate Dividend Policy and the Partial Adjustment Model Michael T. Bond and Mbodja Mougou~
This article critiques Lintner's partial adjustment dividend model in terms of characterizing corporate dividend policy. It is first shown that many combinations of target rates and speeds of adjustment will produce the same stream of cash dividends over time. It is then established empirically from earnings and dividend data that the partial adjustment model gives results that are not unique.
I. Introduction Dividend policy has long been a subject of interest to firms, their stockholders, analysts, and academic researchers.t Aspects of dividend policy that have been examined include the implications of differential taxation of dividends and capital gains (Miller and Modigliani 1961), uncertainty about retention as opposed to cash payments to shareholders (Gordon 1962), preferred habitats of stockholders (Miller and Modigliani 1961), and optimal payment ratios (Walter 1963), and the adjustment process in reaching an optimal payout ratio (Lintner 1956). The last topic, the adjustment process in moving to a desired dividend payont ratio, is the subject of this research. In particular, this study will examine whether the speed of adjustment and target dividend payout rates implied in the partial adjustment model are in fact an accurate characterization of corporate dividend policy.
II. Literature Review There is considerable literature on the adjustment process of firms to a target level of dividends. For example, Lintner (1956) argued that investors will welcome the decision of a firm to change its dividends only if the dividends are related to the firm's earnings or some other public information pertaining to the company. He reasoned that a corporation would have a target dividend payout ratio based on the company's policy regarding internal financing and the cash requirements of its owners. Because many firms are concerned that dividends be stable and because forecasting earnings is
Address reprint requests to Michael T. Bond, PhD, or Mbodja Mougou~, PhD, Department of Finance, Cleveland State University, Cleveland, Ohio 44115. i See, for example, James S. Ang (1987) for an excellent review of the literature on the dividend debate.
Journal of Economicsand Business © 1991 Temple UniversiW
0148-6195/91/$03.50
M.T. Bond and M. Mougou6
166
difficult, Lintner argued that a corporation would adjust the amount paid shareholders over a period of time rather than abruptly. He thus characterized dividend policy by a target payout ratio, that is, a percentage of earnings per share (EPS) and the percentage adjustment to that target rate in each time period. Using aggregated data on corporate earnings and dividends, Lintner tested his proposition empirically and found that the partial adjustment model predicted dividend payments more accurately than "naive" models. Additional research on the partial adjustment model was carried out by Fama and Babiak (1968) (henceforth FB). Using data on individual firms over a 20 year period, FB tested Lintner's propositions and reported a mean speed of adjustment of 0.32 and a sample target ratio of 0.52. FB also examined several alternative dividend models and concluded that Lintner's model predicts dividends better than other models tested. Later research on the partial adjustment model by Fama (1974) indicated roughly the same findings as the FB study. In line with the assertions of Lintner (1956), the results of the work of Sibley and Hobson (1979) indicated that the partial adjustment model explained a higher portion of bank dividend changes than did several other forecasting models. Partington (1984) confirmed that firms apparently targeted dividend payout ratios. Using a survey of 93 large companies, he determined that around 60% of the firms had an explicit target payout ratio, the objective being to distribute about half of the firm's profits as dividends. Partington also reported that approximately, one third of all firms he studied had altered their targets significantly over the 1965-1980 time period. Baker, Edelman, and Farrelly (1985) sampled corporate financial managers on dividend policy. Analysis of the survey indicated that the primary determinants of dividend policy were quite similar to those suggested by Lintner (1956), specifically that firms target a payout ratio and adjust to it slowly over time. Farrelly and Baker (1989) also conducted a survey of institutional investors. Their findings indicated that these sophisticated investors believe that dividend policy affects stock prices and that, in line with the Lintner hypothesis, dividend consistency is of utmost importance. Recently, Bowers, Moran, and Forbes (1987) (henceforth BMF) have challenged the assertions of Lintner (1956) and Fama (1974) with regard to the partial adjustment model. They argue that the partial adjustment model is useful only if the differences in estimated parameters reflect meaningful differences in corporate dividend policy. They then show that dividend payments produced by any target rate and speed of adjustment can be duplicated by using an infinite number of alternative parameter pairs. On the basis of these results, BMF conclude that the partial adjustment model is not useful in explaining corporate dividend policy. The present study will apply the methodology proposed by BMF to earnings and dividend data from a sample of U.S. manufacturing firms to ascertain if the partial adjustment model is an accurate characterization of their dividend policy formulation.
III. The Partial Adjustment Model The partial adjustment model suggested by Lintner (1956) assumes the target level of dividends is given by (1): D*=rE
t
0 < r _ < 1,
(1)
where D* represents the optimal value of dividends associated with the current level of
Dividend Policy and the Partial Admustment Policy
167
earnings Et, and r is the target and, presumably, optimal payout ratio. The change in dividends as a firm moves to the target payout rate is given in (2): Dt - Dr-, = C(D*t - Dt-1) + (t
0 < c <- 1;
(2)
where c is the speed of adjustment and {~t} is an iid innovation sequence. Substituting and moving the lagged term to the right side of the equality in (2) results in (3): (3)
D t = ( c r ) E t + (1 - c ) D , _ , + ~t.
Previous work on the partial adjustment model essentially involved estimating the parameters of (3) and then a discussion on implied dividend policy in the context of the estimated values of c and r. This analysis is meaningful if a given stream of earnings and dividends implies unique values of c and r. If, however, consecutive earnings are related in a linear manner, as shown in (4), an infinite number of c and r pairs will produce the same dividend stream: E t = (1 + g ) E , _ 1,
(4)
where g is a constant growth rate. Recursive substitution for lagged dividends in (3) gives an infinite distributed lagged model, seen in (5): D, = ( c r ) E , + (1 - c ) ( c f ) E t _ 1 41- (1 - c)2(cr)Et_2 + . . . +~t.
(5)
If (4) holds through time, (5) may be expressed as (6): Oo
D, = ( c r ) E o ~
(1 + g ) t - i ( 1
- c ) i ~ t- ~,.
(6)
i=0
By recognizing the equality in (7),
i=0
(1 + g ) ' - l ( l
•
- c)'=
[(1 + g)'l
[(c+g)/(1
+g)]'
(7)
(6) can be expressed as (8):
[(1 + g)'] Dr= (cr)E°[(c+g)/(1
+g)]
+~t"
(8)
Given the equality in (4), dividends in period t can be expressed as (9): O t =
e t ( c r ) / [ ( c + g ) / ( 1 + g)] + ~t.
(9)
Given a constant growth in earnings it is obvious that there is a one-for-one relationship between dividends and the partial adjustment policy. Division of both sides
M. T. Bond and M. Mougou6
165
Table 1. Earnings and Dividends for the Constant Growth Partial Adjustment Model (E~ = $1,000, g = 5%, c = 25%, r = 40%) Period
Earnings
Dividends
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
$1,000.00 1,050.00 1,102.50 1,157.63 1,215.51 1,276.28 1,340.10 1,407.10 1,477.46 1,551.33 1,628.89 1,710.34 1,795.86 1,885.65 1,979.93 2,078.93 2,182.87 2,292.02 2,406.62 2,526.95
$350.00 367.50 385.88 405.17 425.43 446.70 469.03 492.49 517. l 1 542.97 570.11 598.62 628.55 659.98 692.98 727.63 764.00 802.21 842.32 884.43
N o t e . E t is earnings at time t ffi 1, g is a constant growth rate, c is the speed of adjustment in the partial adjustment model, and r is the assumed target payout rate.
by current earnings gives (10):
D,I , =
+ g)/(1 + g)] +
(10)
where et is a function of ~t and is also iid. Given that g is a constant and that the c and r terms are established by the firm's management, dividends will be a constant portion of earnings over time. If the dividend payout ratio D / E is defined as k, (10) becomes (11):
k = ( c r ) / [ ( c + g ) / ( 1 + g)] + ~t, E(k) = (cr)/[(c + g)/(1 + g)],
and
(11) (12)
where E(k) is the expected value of k, the payout ratio. Given the equality in (4), no single c and r pair will uniquely describe the firm's series of dividends or its payout ratio over time. For example, assume earnings at t = 1 are $1,000 and g = 5 percent. Assume a target payout rate of 40 percent and a speed of adjustment of 25 percent. Dividends, as implied by (9), are 35 percent of earnings in each period. Dividends based on these values are generated for a 20-year period and are reported in Table 1. A set of alternative target rate and speed of adjustment pairs that produce the same dividends as r = 40 percent and c = 25 percent can be found by setting k = 35 percent, g = 5 percent, allowing c to vary from - 1 to 1, and solving (9) for r. Figure 1 and Table 2 present these solution pairs. It is easily shown that they produce the same dividends as the initial c-r pair if applied to any earnings stream. Note that the asymptotic relationship between c and r values in Figure 1 is consistent with the above data. The latter observation lends additional support to the assertion of BMF that there are many c and r pairs, that are consistent with the partial adjustment model. It should
169
Dividend Policy and the Partial Admustmem Policy Ill
1.00
0.75 C 0.50
0.25
0-00
o.25
o:'3o
o:35
o:,o
o. ,5
o:5o
o.55
R Figure 1. Graph of
c-r
pairs for hypothetical 5 percent g, .35 payout.
be recognized that the above analysis does not imply that the partial adjustment model is not useful in forecasting dividend payments. Rather, it suggests that firms that exhibit autoregression in earnings over time can produce the same dividend payout ratio with an infinite combination of c - r values. The implication for firms in the autoregressive category, then, is that a particular c - r value is not the only policy combination that will produce the firm's desired payout ratio. It then follows that statistical estimates of the c - r values in Lintner's model may not be unique measures of corporate dividend policy. The present study examines the applicability of the BMF hypothesis to corporate dividend policy.
IV. The Empirical Results The Data Annual data from the Compustat tapes were collected for a sample of U.S. manufacturing firms. Annual data are used instead of quarterly data because of the relative inertia in quarterly dividend payments and because the time-series literature on interim corporate earnings has concluded that quarterly earnings contain significant amounts of
M. T. Bond and M. M o u g o u 6
170
T a b l e 2. Equivalent Partial Adjustment Policies ( k = 3 5 % , g = 5%) c -
1.00 -0.90 -0.80 - 0.70 0.60 - 0.50 0.40 - 0.30 - 0.20 -0.10 0.00 0.10 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 -
-
r .3166 .3148 .3125 .3095 .3055 .3000 .2916 .2777 .2500 .1666 Undefined .5000 .4166 .4000 .3888 .3750 .3666 .3611 .3571 .3541 .3518 .3500
Note. k is the actual payout ratio, g is a constant growth rate, c is the speed of adjustment in the partial adjustment model, and r is the implied target payout rate .......
noise or possess seasonal characteristics. 2 These factors could obscure existing relationships and lead to spurious results. The use of annual data is likely to minimize these problems. The sample was limited to firms reporting positive earnings (net income before extraordinary items) and having paid dividends every year over the 1968-1987 20-year time period covered in the present study. These criteria results in 430 firms.
Testing the Hypothesis
BMF essentially assert that if any c and r pair fits a firm's dividends and earnings pattern and earnings are determined autoregressively over time, then there will be many c and r pairs that fit the data. Using the Box and Jenkins (1976) procedure and the Augmented Dickey-Fuller test for unit roots as described in Engle and Granger (1987) resulted in the finding that only 310 of the 430 firms selected had earnings series behavior that follows AR(1) stationary processes. Our final sample thus includes only these 310 firms whose earnings exhibited significant first-order autocorrelation. For each of the 310 firms in the final sample the correlation coefficient between E t and Dr-i was also calculated. Figure 2 shows the frequency distribution of the simple correlation coefficient between E t and D t_ 1 for these sample firms. Clearly, high levels of correlation are present between E t and D t_ l, the explanatory variables of the
2 See, for example, Brown and Rozeff (1979), Foster (1977), Griffin (1977), and Lorek (1979).
Dividend Policy and the Partial Admustment Policy
171
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172
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0.7 ÷ 4" 4-
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partial adjustment model. 3 As is always the case, the question whether the resulting multicoUinearity problem is sufficient to impair the usefulness of the model is an empirical one. For example, multicollinearity frequently results in high standard errors of the estimates and correspondingly low t statistics; however, as noted by Maddala (1977), it is possible to have statistically significant t statistics even in the presence of high degrees of multicollinearity. The results of this correlation can be seen when the 310 firms in the final sample are divided into 2~) mutually exclusive groups by the most recent payout ratio, k. Firms with 0 < k < .05 are placed in Group 1, those with .05 < k < . 10 are assigned to the next group and so on. Figures 3-11 are plots of the c - r pairs from the payout groups with the most observations (k between .35 and .40, .40 and .45, .45 and .50, .50 and .55, .55 and .60, .60 and .65, .65 and .70, .70 and .75, .75 and .80). The plots have
3 Casual observation of the high versus low correlation firms indicated no easily identifiable variables (i.e., earnings growth, industry classification, etc.) that explain the difference in correlation values between E t and Dr_ j.
Dividend Policy and the Partial Admusunent Policy
173
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Figure $. Relationship between
c-r l~drs
for .45-.5 payout ratios.
174
M.T. Bond and M. Mougou6
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Figure 7. Relationship between
c-r
pairs for .55-.6 payout ratios.
Dividend Policy and the Partial Admustment Policy
175
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c-r
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1.25.
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÷ 4.
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c-r
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176
M.T. Bond and M. Mougoud
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Figure 11. Relationship between
c-r
pairs for .75-.8 payout ratios.
Dividend Policy and the Partial Admustment Policy
177
two distinct features. First, many disparate c-r pairs are associated with roughly the same ex post payout ratio. Second, the c-r pairs in each figure roughly conform to the hyperbolic function of Figure 1. The constant-growth model proposed by BMF suggests that even though the partial adjustment model produces disparate parameter estimates, there may be no statistically significant difference in the dividend policies of these firms. The groups shown in Figures 3-11 are used to carry out further tests because they have the largest number of firms with similar ex post dividend payout ratio. The hypothesis that each firm's payout ratio is significantly different from the mean for each of these groups was examined. In each case the hypothesis that the difference is zero could not be rejected at the 5 percent level of significance. Because it may be possible that the empirical results reported here are sensitive to industry variations, the data were broken down by two-digit SIC industry codes with the requirement that each industry be composed of at least 20 firms. In this fashion, seven two-digit industries comprising approximately 46 percent of the sample were identified. The results were then summarized and analyzed on the basis of each industry. The empirical results were substantially the same as for all industries together. These findings lead to the tentative conclusion that the empirical results reported in the present study are robust to industry variations. In addition, the above results have important implications for investors. Those seeking a particular stream of cash dividends over time appear to have far more firm "choices" in companies able to produce their desired cash stream. Tables 1 and 2 clearly show that any of the values of target payout rate and speed of adjustment from a firm with a 5 percent earnings growth could provide the investor with the 35 percent payout ratio that is shown.
V. Conclusion This article demonstrates that two potential problems exist when the partial adjustment model is used to characterize the dividend policy of the individual firm. The first of these is that high degrees of correlation between the independent variables of the partial adjustment model may render the empirical results of such a model useless. This study also shows that autocorrelated earnings of firms result in an infinite number of pairs of speeds of adjustment and target payout rates that give identical dividend payout streams. Empirical tests with representative firms indicated that in many cases the partial adjustment model gives results that are not unique. It is probable, then, for the firms under consideration in this study, that the partial adjustment model does not generate unique measures of the dividend policy of the individual firm.
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178
M.T. Bond and M. Mougou6 Brown, L. D., and Roseff, M. S. Spring 1979. Univariate time-series models of quarterly accounting earnings per share: A proposed model. Journal of Accounting Research 17: 179-189. Engle, R. F., and Granger, C. W. J. 1987. Co-integration and error correction: Representation, estimation, and testing. Econometrica 55:251-276. Fama, E. June 1974. The empirical relationship between the dividend and investment decisions of firms. American Economic Review 64: 304-318. Fama, E., and Babiak, H. December 1968. Dividend policy: An empirical analysis. Journal of the American Statistical Association: 1132-1161. Farrelly, G., and Baker, K. Summer 1989. Corporate dividends: View of institutional investors. Akron Business and Economic Review 20: 89-100. Foster, G. January 1977. Quarterly accounting data: Time-series properties and predictive ability results. Accounting Review 52: 1-21. Gordon, M. 1962. The Investment, Financing, and Valuation of the Corporation. Homewood, Ill.): R. D. Irwin. Griffin, P. Spring 1977. The time-series behavior of quarterly earnings: Preliminary evidence. Journal o f Accounting Research 15: 71-83. Lintner, J. May 1956. Distribution of incomes of corporations among dividends, retained earnings, and taxes. American Economic Review 46: 97-113. Lorek, K. S. Spring 1979. Predicting annual net earnings with quarterly earnings time-series models. Journal of Accounting Research 16: 190-204. Maddala, G. S. 1977. Econometrics, New York: McGraw-Hill. Miller, M., and Modigliani, F. October 1961. Dividend policy, growth, and the valuation of shares. Journal of Business 34: 411-433. Partington, G. November 1984. Dividend policy and target payout rates. Accounting and Finance 24: 63-74. Sibley, A., and Hobson, H. Spring 1979. A test of selected models of bank dividend policy. Akron Business and Economic Review 10: 29-34. Walter, J. May 1963. Dividend policy: It's influence on the value of the enterprise. Journal of Finance: 280-291.